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Q.

An airplane when flying at a height of $3125 m$ from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are $30 °$ and $60 °$ respectively. Find the distance between the two planes at that instant.

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a

6350 m

b

6550 m

c

6250 m

d

6450 m

answer is A.

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Detailed Solution

Given that an airplane when flying at a height of 3125m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are

30 °

and

60 °

respectively.
We have to find the distance between the two planes at that instant.
Consider C and D be the position of the two planes and A be the point observation.
An aeroplane when 3000 m high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 60 ^

An aeroplane when 3000 m high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 60 ^

∠ CAB = 30 °, ∠ DAB = 60 °, BC = 3125 m

Let

DC = y m, AB = xm .

In right

Δ ABC,

tan 30 ° = BC AB

⇒ 13 = 3125 x

∴ x = 31253

In right

Δ ABD,

tan 60 ° = BD AB

⇒ 3 = y+3125 31253

⇒ 9375 = y + 3125

∴ y = 6250 m

Therefore, the distance between the two planes is

6250 m

.
Therefore, the correct option is 1.

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